Continuity & Bernoulli worksheet with answers

Free printable Continuity & Bernoulli worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
12d1​ = 75 mm, v1​ = 2 m/sd2​ = 40 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 2 m/s
Q = L/s
2.Easy
12d = 50 mm, v = 0.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 0.75 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 0.75 m/sd = 50 mm
ṁ = kg/s
3.Medium
12d1​ = 80 mm, p1​ = ?d2​ = 40 mm, p2​ = 50 kPa

Water flows at 11 L/s through a horizontal pipe that narrows from 80 mm to 40 mm. The pressure in the narrow section is 50 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 11 L/sd1 = 80 mmd2 = 40 mmp2 = 50 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 400 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 400 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 400 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 6 m. At section 1 the pressure is 350 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 350 kPav1 = 3 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 100 mmp1​ = 40 kPad2​ = 30 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 100 mm and a gauge pressure of 40 kPa. The nozzle exit diameter is 30 mm, and the height difference across the nozzle is negligible. Ignoring losses and air resistance, find the height H the jet rises above the nozzle. Use g = 9.81 m/s².

d1 = 100 mmp1 = 40 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. Q = 8.836 L/s
  2. 2. ṁ = 1.296 kg/s
  3. 3. p1 = 85.92 kPa
  4. 4. p2 = 382.6 kPa
  5. 5. p2 = 272.9 kPa
  6. 6. H = 4.111 m

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